SVM的几何方法—SK类思路的研究

Study on geometric approach of SVM algorithm——SK algorithm analysis and study

支持向量机(Support Vector Machine,SVM)的几何方法是一种基于SVM计算过程中几何意义出发的求解方法。利用其几何特点,比较直观地对其基本算法的构建过程进行了分析。两凸包相对位置可以简要地归纳成5类,且在该类算法迭代过程最优点多在顶点和边界上,该类算法在第一次迭代就可能达到边界(最优点);该类算法的手动单步模拟计结果揭示:很多情况下,该类算法迭代过程的投影并不成功,虽不影响解法的最终结果,但会影响迭代效率;基于几何的分析,给出软SK软算法的两种改进思路(Backward-SK和Forward-SK思路),并进行了仿真比较计算。实验表明,该方法计算效果与原思路相似,但是计算过程理解更加直观。

The geometric approach of the Support Vector Machine（SVM） is a kind of geometric way to find the solution to the problem of the SVM algorithm.Based on its geometric characters,the SK（Schlesinger-Kozinec） algorithm is studied intuitively. It briefly sums up the two convex hulls,based on their relative positions,into five categories,and makes sure their optimizing position got in each computing is mostly at the hull vertices or boundary,it can get to the boundary（the optimization place of the computing） at the first computation.The manual single-step simulation results show that the projection is not always successful for such kind of algorithms in many cases,though it can’t affect the computing result,but can weaken the algorithm efficiency.Based on the analysis,it demonstrates two improving ways for the soft SK algorithm（Backward-SK and Forward-SK methods）,and makes some simulation for comparing.The simulation results show that the improved method computing results are almost same as the SK and soft SK ones,but the computing process of improved one is more intuitive.